Question

Use Heron's Formula, that is, the area of a triangle is A = s(s-a)(s-b)(s-c), where thetriangle contains sides a, b and c and s= }(a+b+c) to find the area of the triangle with sidelengths: a = 4, b = 3, C = 6.5.3 square units6 square units12 square units9 square units

Answer 1

Heron's formula makes use of s, which is described as the semi-perimeter of the triangle. Before we can use Heron's formula, let us solve first for the value of s via the equation

`s=(1)/(2)(a+b+c)`

The lengths of the triangle are given in the problem. Just plug it in on the equation above and compute.

`s=(1)/(2)(4+3+6)=(13)/(2)`

Now, let's move on using Heron's formula to solve the area of the triangle. We have

`\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ A=\sqrt[\square]{(13)/(2)((13)/(2)-4)((13)/(2)-3)((13)/(2)-6)_{}} \\ A=\sqrt[]{(13)/(2)\lbrack((5)/(2)*(7)/(2)*(1)/(2))\rbrack} \\ A=\sqrt[]{(13)/(2)((35)/(8))} \\ A=\sqrt[]{(455)/(16)}=5.33 \end{gathered}`

Therefore, the area of the triangle is 5.3 square units.